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タイトル: 38. Theoretical Seismograms of Spheroidal Type on the Surface of a Gravitating Elastic Sphere : 3. Case of a Homogeneous Mantle with a Liquid Core
その他のタイトル: 38.重力均衡下にある弾性球の表面を伝わるスフェロイド型振動 : 3.流体核をもつ等方等質マントルの場合
著者: Usami, Tatsuo
Sato, Yasuo
Landisman, Mark
Odaka, Toshikazu
著者(別言語): 宇佐美, 龍夫
佐藤, 泰夫
小高, 俊一
発行日: 1968年10月31日
出版者: 東京大学地震研究所
掲載誌情報: 東京大学地震研究所彙報. 第46冊第4号, 1968.10.31, pp. 791-819
抄録: Theoretical seismograms of spheroidal disturbances on the surface of an elastic sphere consisting of a homogeneous mantle and a liquid core are calculated when uniform radial stress is applied to a small circle around the pole. The effect of gravity is taken into consideration. Contributions are included from the free spheroidal oscillations of the first few radial modes for all orders with periods larger than 12 sec. The results of these computations are compared with the corresponding quantities for the case excluding the effect of gravity. Noteworthy results from the study of spheroidal disturbances propagating on the surface of a gravitating elastic sphere with a homogeneous mantle and a liquid core, when the uniform radial stress is applied to a circular area around the pole, are : 1. The difference between non-dimensional frequency for the present case and for the case excluding the effect of gravity is not a simple function. The discrepancy is large for modes lying along the branch specified by i=1'; it tends toward negligible values as the order number increases. 2. The corresponding phase and group velocities exhibit their greatest differences for the first three radial modes and for orders less than about 15. The number of maxima and minima for the group velocity curves increases with radial mode number i. Curves connecting corresponding maxima and minima tend toward the value U/VS0=≒1.2 as the period decreases to zero; in the case of the homogeneous sphere these curves approach 1.3. 3. The amplitudes of the Common Spectrum suggest that higher radial modes with i≠10 may still give appreciable contributions to the theoretical seismogram. 4. The Rayleigh wave shows a simple disturbance consisting of approximately one cycle of oscillation. The pattern of wave propagation can be explained by the concept of dispersion. 5. The convergence of the wave form of the P wave by the successive addition of radial higher modes is not so rapid as in the case without gravity. The slower convergence is caused by the difference of the time and space functions of the applied forces and by the minimum values of period employed in the synthesis. 6. The orbital motion of the Rayleigh wave shows a phase advance of π/2 near the antipode. 7. In the seismograms showing body waves, the surface-reflected S waves end abruptly near the travel time of a wave propagating along the surface with the shear wave velocity. 8. The variation of amplitude of the body waves as a function of epicentral distance can be explained by the theory of the divergence factor, after accounting for the effect of reflection at the surface.K49|1.我々は弾性球の自由振動周期や理論地震記象に及ぼす重力の影響を研究して来たが,その第3報として,流体核のある等方等質マントルの場合のスフェロイド型振動の理論地震記象を作つた.方法は従来と同じで,変位をいろいろな固有振動のモードの和として表わした.
URI: http://hdl.handle.net/2261/12409
ISSN: 00408972


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